The non-trivial magnon band topology and its consequent responses have been extensively studied in two-dimensional magnetism. However, the triangular lattice antiferromagnet, the most well-known geometrically frustrated magnetic system, has received less attention than the other well-known frustrated lattice, such as the Kagome system from the perspective of magnon band topology. It is because of the spin-chirality cancellation in the undistorted the triangular lattice antiferromagnet. In this work, we study the band topology and the thermal Hall effect of the triangular lattice antiferromagnet with (anti-)trimerization distortion using the linear spin-wave theory. We show that the spin-chirality cancellation is removed in such a case, giving rise to the non-trivial magnon band topology and the finite thermal Hall effect under the external perpendicular magnetic field. Moreover, the magnon bands exhibit band topology transitions tuned by the magnetic field. We demonstrate that band topology transitions are accompanied by the logarithmic divergence of the first derivative of the thermal Hall conductivity. Finally, we examine the above consequences by calculating the thermal Hall effect in the hexagonal manganite YMnO3, well known to have anti-trimerization.[1] Kyung-Su Kim, Ki Hoon Lee, Suk Bum Chung, and Je-Geun Park PRB 100, 064412 (2019)